What is being asked here: prove that if 2 triangles have sides perpendicular each to each, then the triangles are similar.
If 2 angles have sides either parallel or perpendicular each to each, then the angles are either equal of supplementary. (Draw a figure and you will understand the truth of this statement!)
3 pairs supplementary leads to the contradiction that the sum of the angles in the 2 triangles exceeds 360 degrees.
2 pairs supplementary leads to the same contradiction.
This means 2 of the pairs of angles are equal. This implies that all 3 angles are equal and, therefore, the triangles are similar.
